What’s in a name? That which we call calculus.


There’s a great poetry in the way calculus deconstructs the universe; and in some sense, it’s much the same as Shakespeare. 

Shakespeare takes archetypical characters from the world and puts them on a stage with a complication, and slowly, over the course of five acts, watches as complex human interactions unwind and untangle, eventually gushing great tides of reason and beauty over his audience. The only difference between the Bards work and the mathematical study of change, is that the characters are ideas, the stage is the mind and the five acts are the processes of finding a limit.

What else do Shakespeare and calculus have in common? On the surface, they actually have quite a lot. Both were written over three centuries ago – Shakespeare in the 16th century and Newton in the 17th (acknowledging the Leibniz contribution of course). They’re also both written in a language that at first seems entirely indecipherable but eventually speaks meaning. For these two reasons they are also wildly unpopular for students and attract a lot of criticism for their use in the classroom.

The defence though is to encourage the academically curious and foster a broad education. It is true that Shakespeare won’t greatly improve your ability to write an e-mail or advertise a new product. Similarly calculus won’t help you budget for groceries or pay your taxes. But they do broaden your awareness to the nature of humanity and that of the universe; they will allow you to adapt to an ever changing society and economy. Essentially they enlighten the mind, and this is almost the exact reason why we live in a post-enlightenment era – an era of reason and learning.

Calculus takes up a special part in my life. Not only does it drive the world I study but it also illuminates the universe I live in. The study of marginal change and its effect on broader outcomes is the world I research, that of decisions, choice and optimisation – otherwise known as human behaviour. But beyond this, looking at the effect of infinitesimal change is essentially the study of evolutionary processes, physical systems, biochemical reactions and much more.

A few weeks back a professor of mine, Martin Richardson, drew on this comparison when expressing his disdain for students, nay people, who are proud of being innumerate when it comes to differentials. His point was that academically minded people don’t tend to gloat about not having read Shakespeare, a core component of a modern liberal education, but when it comes to calculus, despite the significant role it plays in nearly every facet of our society, they somehow find moral superiority in their ignorance.

The more I research this idea, the more truth I find in its proposition. Aside from the shear practicality of learning the principals of calculus, the reasons for teaching it to students are the same as those for teaching Shakespeare. While written a long time ago in a language difficult to decipher, the study of differences contains profound insights into the world around us and unlocks beauty in the most medial of life’s moments. An appreciation of its mighty contribution to the theoretical and applied sciences gives us an ability to respond, adapt and learn – the core principals of a true liberal education. Beyond high school, pride in an ignorance of dy/dx, and more broadly mathematics, is pride in a life that ignores this poetry in nature and is something to be pitied not revered.

Update 24/06/15:

Almost minutes after I posted this piece I watched a video from Numberphile on Klein Bottles where Brady (the producer) interviewed Cliff Stoll, a famous science communicator and researcher. His serendipitous opening quote was simply amazing [watch it here]:

Math ain’t about numbers. If you think math is about numbers; you probably think that Shakespeare is all about words, you probably think dancing is all about shoes, you probably think music is all about notes. Math ain’t about numbers; it’s about logic, it’s about beauty, it’s about connections, it’s about how you get from one place to another.


2 thoughts on “What’s in a name? That which we call calculus.

  1. I was hoping to finish this discussion off with a good recommendation of an adult book to read that introduces academically minded people to calculus without much of the unnecessary jargon and exercises for application. Alas, I don’t have one, and I will make it my goal to find one (or write one myself). Let me know if you know of any!

  2. Plato’s Mathematical Imagination, by Robert S. Brumbaugh
    The Divine Proportion, by H. E. Huntley. (There are nontrivial mistakes in the illustration in this book, but all in all its description of beauty is very good.)
    A Mathematician’s Apology, by G. H. Hardy (Never got a chance to take a look, but always try to do so.)
    BTW, I like your post.

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